The literature on optimal monetary policy typically makes three major assumptions: 1) policymakers’ preferences are quadratic, 2) the economy is linear, and 3) stochastic shocks and policymakers’ prior beliefs about unobserved variables are normally distributed. This paper relaxes...

We consider a noisy observed vector y=x+u∈Rn. The unobserved vector x is a solution of a non-invertible linear system Ax=v, where v is a forcing term. A unique solution of the system is obtained by considering additional constraint on the vector x. This constraint is defined by a triple...

A time-varying probability density function, or the corresponding cumulative distribution function, may be estimated nonparametrically by using a kernel and weighting the observations using schemes derived from time series modelling. The parameters, including the bandwidth, may be estimated by...

Modelers frequently assume (either implicitly or explicitly) that an agent’s posterior expectation of some variable lies between their prior mean and the realization of an unbiased signal of that variable. We call this property updating toward the signal (UTS). We show that if the prior and...